Just when Democratic advocates of tax simplification thought they were taking back some of the political initiative from President Reagan, a potentially more divisive problem has arisen: growing Democratic support in Congress for a new minimum tax.

The minimum tax, which emerged with new force when Congress returned from its Easter recess, has all the elements of classic Democratic "bad-guy liberalism," in which a "bad guy" is identified and defeated.

The minimum tax, in its various forms, would prevent big corporations or wealthy individuals from avoiding taxes through the more than a hundred shelters, deductions and exemptions in the tax code. If it picks up a little extra revenue in a time of big deficits without looking like a tax increase, so much the better.

But the emergence of the minimum tax as an issue is significant for what it may tell about the Democratic Party and how it sees its political future. For the minimum tax clearly is linked to questions of realignment politics, the 1986 midterm elections, internal House politics and the power of special interests.

Democratic advocates of comprehensive tax reform are plainly worried that the minimum tax may be the perfect cover for colleagues who prefer to duck the tough fight ahead over tax simplification.

"The minimum tax at this point is almost seditious in its impact on tax reform," said an aide to a leading House Democrat.

House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), whose strong support for enacting a tax simplification bill this year has helped give the issue momentum, was concerned enough about implications of the minimum tax that he delivered a stern warning to its supporters in a speech Friday in Chicago.

"To reformers, the substitution of a minimum tax for comprehensive reform is a cop-out," Rostenkowski said, according to a text of the speech made available here. "Even though toughening the existing minimum tax would weaken the impact on preferences, it would not erase them. The weeds would be topped, but the roots would remain."

Democrats have been complaining for months that Reagan may have stolen one of the great political issues of the time by embracing tax simplification. Lately, some party leaders have been trying to regain the political initiative on the issue -- or at least balance things a little better.

Sen. Bill Bradley (D-N.J.) and Rep. Richard A. Gephardt (D-Mo.), who introduced the first comprehensive tax simplification bill three years ago, have been stumping for the bill around the country. And last week, Democratic National Chairman Paul G. Kirk Jr. sent out a fund-raising appeal, asking big donors to provide a $270,000 kitty to help win approval of the Bradley-Gephardt "fair tax."

"We Democrats realize that a good tax simplification plan can stimulate economic growth, treat middle-class taxpayers more fairly, make our economy more rational and ensure that our industries are competitive in an increasingly tough international marketplace," Kirk wrote.

All that has taken place, however, against growing suspicion among some Democrats that they are about to be snookered on the tax simplification issue. "What's in it for us?" is a question increasingly being asked in Democratic leadership meetings, according to several House Democratic aides.

The fear among these Democrats is that Reagan and the Republicans will reap the political benefits from any bill approved by Congress this year, while Democrats could end up alienating longtime allies in the labor movement (which opposes taxation of fringe benefits) or drying up campaign contributions from the oil and gas industry (which could lose many of its preferences).

That has put Rostenkowski in a politically difficult spot, because he is the key Democratic link to Treasury Secretary James A. Baker III, who is putting together the administration's proposal.

The recent promotion of the minimum-tax concept by House Majority Leader James C. Wright Jr. (D-Tex.) is seen by some House Democrats as part of an ongoing friction with Rostenkowski, who continues to make noises about challenging Wright for speaker in two years.

Labor's influence on the issue appears significant. "In the last few months, there has been a lot of worry about fringes," the aide to a powerful Democratic senator said last week. "They labor have gotten no satisfaction from Bradley, and they have no confidence that Rostenkowski is listening."

Some Democrats appear reluctant to offend labor, fearing the loss of financial support in future elections. "The threat is there," said an aide to one House proponent of tax reform.

"As tax reform has gained more interest, people are really getting hurt by the lobbies," Gephardt said. "And it's just beginning." Gephardt was not talking specifically about labor, however.

"This is no longer a benign idea," said another Democrat. "People are choosing up sides."

The minimum tax appeals to many Democrats -- and some Republicans -- because it appears to solve the worst abuses of the tax system without inflicting the pain of comprehensive reform. And Democrats who fear Reagan's retribution for proposing a tax increase find the minimum tax a painless revenue raiser.

"We do not propose to raise taxes. We propose to begin to collect taxes," said Sen. Daniel Patrick Moynihan (D-N.Y.), cosponsor of one minimum-tax bill with Sen. John H. Chafee (R-R.I.).

That's where 1986 politics comes into play. Democratic political strategists say they would happily defend the minimum tax -- "A sure winner," one Democrat called it -- in next year's campaign while blasting Reagan and the Republicans for trying to lower Social Security benefits.

"That's the best of both worlds," one political operative said. "A campaign manager like me would love that."

But Democratic proponents of tax simplification fear that the party is pursuing a strategy of short-term political gain if the minimum tax derails the drive to rewrite the tax code. What could be lost, they argue, is the longer-term payoff of reorienting the party away from the politics of redistribution.

They say public outrage over corporations that pay no taxes is needed to help combat powerful special interests in the fight over tax simplification. "To some special interests, a tougher minimum tax is a godsend," Rostenkowski said.

Whether proponents of the minimum tax are trying to protect their favorite interest groups or simply seeking to make certain that big corporations pay some tax, the issue's emergence has put the Democratic Party on the spot. The outcome will be a powerful indicator of the direction Democratic leaders believe they should take in seeking to restore their party to power.